A motorcycle is moving at the speed of 25 km/hr and its speed is increased by 7 km/hr at the end of each hour. How much time it will take to cover a distance of 225 km?

Options

A. `(11/2)hr`
B. 7hr
C. `(13/2)hr`
D. `6hr`

Answer

To solve the problem step by step, we will calculate the distance covered by the motorcycle in each hour until it reaches a total distance of 225 km.

### Step 1: Identify the initial speed and the speed increase
- The initial speed of the motorcycle is 25 km/hr.
- The speed increases by 7 km/hr at the end of each hour.

### Step 2: Calculate the distance covered in each hour
1. **First Hour:**
- Speed = 25 km/hr
- Distance covered = Speed × Time = 25 km/hr × 1 hr = 25 km

2. **Second Hour:**
- Speed = 25 km/hr + 7 km/hr = 32 km/hr
- Distance covered = 32 km/hr × 1 hr = 32 km

3. **Third Hour:**
- Speed = 32 km/hr + 7 km/hr = 39 km/hr
- Distance covered = 39 km/hr × 1 hr = 39 km

4. **Fourth Hour:**
- Speed = 39 km/hr + 7 km/hr = 46 km/hr
- Distance covered = 46 km/hr × 1 hr = 46 km

5. **Fifth Hour:**
- Speed = 46 km/hr + 7 km/hr = 53 km/hr
- Distance covered = 53 km/hr × 1 hr = 53 km

6. **Sixth Hour:**
- Speed = 53 km/hr + 7 km/hr = 60 km/hr
- Distance covered = 60 km/hr × 1 hr = 60 km

### Step 3: Calculate the total distance covered in the first five hours
- Total distance covered in the first five hours:
- Distance = 25 km + 32 km + 39 km + 46 km + 53 km
- Total distance = 195 km

### Step 4: Calculate the remaining distance to cover
- Total distance to cover = 225 km
- Remaining distance = 225 km - 195 km = 30 km

### Step 5: Calculate the time to cover the remaining distance
- In the sixth hour, the speed is 60 km/hr.
- Time to cover the remaining 30 km = Distance / Speed = 30 km / 60 km/hr = 0.5 hr

### Step 6: Calculate the total time taken
- Total time = Time for first 5 hours + Time for remaining distance
- Total time = 5 hours + 0.5 hours = 5.5 hours or 11/2 hours

### Final Answer
The total time taken to cover a distance of 225 km is **11/2 hours**.

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